This paper gives a modification of a class of stochastic Runge-Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

In this paper a domain Ω ⊆ C is a connected open set. We let O Ω denote the algebra of holomorphic functions on Ω. We will use the following notation: D denotes the unit disc in the complex plane. We let D2 D × D denote the bidisc, and D D × D × · · · × D the polydisc in C. The symbol B Bn is the unit ball in C. A domainΩ ⊆ C is said to be Runge if any holomorphic f onΩ is the limit, uniformly ...

_________________________________________________ Vernon W. Ruttan is Regents Professor in the Department of Applied Economics and in the Department of Economics at the University of Minnesota. This paper draws on two earlier papers (Ruttan, 1998; in press). I am indebted to Donald N. Duvick, Nicholas Kalaitzandonakes, John M. Reilly, C. Ford Runge, W. Burt Sundquist, and Paul E. Waggoner for c...

This paper presents a new simple technique to improve the order behaviour of Runge-Kutta methods when applied to index 2 DAEs. It is then shown how this can be incorporated into a more eecient version of the code RADAU5 developed by E. Hairer and G. Wanner.

M. N. Gevorkyan,1, * T. R. Velieva,1, † A. V. Korolkova,1, ‡ D. S. Kulyabov,1, 2, S and L. A. Sevastyanov1, 3, ¶ Department of Applied Probability and Informatics Peoples’ Friendship University of Russia Miklukho-Maklaya str. 6, Moscow, 117198, Russia Laboratory of Information Technologies Joint Institute for Nuclear Research Joliot-Curie 6, Dubna, Moscow region, 141980, Russia Bogoliubov Labor...